Association rule mining using max pattern transactions

ABSTRACT

Embodiments of the present invention provide systems and methods for associating rule mining in data comprising first and second variables, by generating a first and second filtering bitmap. The first filtering bitmap represents a set of values for the second variable for each of a plurality of values of the first variable. The second filtering bitmap represents, associations between frequent values of the second variable, which enables the identification of frequent 2-pattern itemsets. Thus, by performing first logical operations on the frequent 2-pattern itemsets, frequent high order-pattern itemsets may be identified. A max pattern itemset may be identified among the frequent high order-pattern itemsets. As a result, embodiments may mitigate performance and stability problems associated with conventional association rule mining approaches.

BACKGROUND

The technical character of the present invention relates generally to the field of data mining, and more particularly, Association Rule Mining (ARM) algorithms.

ARM is a widely used knowledge discovery technique, particularly within the field of data mining. Since the introduction of ARM by Agrawal, ARM has been utilized to identify patterns of data and/or association rules from a large amount of data (e.g., database).

A primary aim of extracting knowledge from databases is to generate a large frequent itemset. However, generating frequent itemsets is a complex task, as it usually exhausts system resources. For instance, generating candidate itemsets and calculating the occurrence of a candidate set in a transaction set, and subsequently in a database involves iterations through the database. Consequently, each iteration requires time and incurs heavy computation cost.

Further, if the data is dynamic (i.e., data of the database changes over time), conventional ARM algorithms need to rescan the entire database. Consequently, a large/high computation cost is incurred and is such conventional approaches are not feasible for real-time applications.

SUMMARY

According to an embodiment of the present invention, a computer-implemented method for association rule mining in data comprising first and second variables each having a set of possible values, the method comprising: generating a first filtering bitmap representing, for each of a plurality of values of the first variable, a set of values for the second variable; generating a second filtering bitmap representing associations between frequent values of the second variable; identifying frequent 2-pattern itemsets in the second filtering bitmap; performing first logical operations on the frequent 2-pattern itemsets to identify frequent high order-pattern itemsets; and identifying a max pattern itemset among the frequent high-order itemsets as a mining result.

According to an embodiment of the present invention, a computer program product for association rule mining in data comprising first and second variables each having a set of possible values, the computer program product comprising a computer readable storage medium having program instructions embodied therewith, the program instructions executable by a processing unit to cause the processing unit to perform a method comprising: generating a first filtering bitmap representing, for each of a plurality of values of the first variable, a set of values for the second variable; generating a second filtering bitmap representing associations between frequent values of the second variable; identifying frequent 2-pattern itemsets in the second filtering bitmap; performing first logical operations on the frequent 2-pattern itemsets to identify frequent higher order-pattern itemsets; and identifying a max pattern itemset among the frequent higher-order itemsets as a mining result.

According to an embodiment of the present invention, a system for association rule mining in data comprising first and second variables each having a set of possible values, the system comprising: a processor arrangement configured to perform the steps of: generating a first filtering bitmap representing, for each of a plurality of values of the first variable, a set of values for the second variable; generating a second filtering bitmap based on frequent values of the second variable; identifying frequent 2-pattern itemsets in the second filtering bitmap; performing first logical operations on the frequent 2-pattern itemsets to identify frequent higher order-pattern itemsets; and identifying a max pattern itemset among the frequent higher-order itemsets as a mining result.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention is described in the detailed description which follows, in reference to the noted plurality of drawings by way of non-limiting examples of exemplary embodiments of the present invention.

FIG. 1 depicts a cloud computing node according to an embodiment of the present invention.

FIG. 2 depicts a cloud computing environment according to embodiments of the present invention.

FIG. 3 depicts abstraction model layers according to embodiments of the present invention.

FIG. 4 depicts a cloud computing note according to another embodiment of the present invention.

FIG. 5 is a simplified flow diagram of a method for association rule mining in data according to an exemplary embodiment.

DETAILED DESCRIPTION

It should be understood the figures are merely schematic and are not drawn to scale. It should also be understood that the same reference numerals are used throughout the figures to indicate the same or similar parts.

In the context of the present application, where embodiments of the present invention constitute a method, it should be understood a method is a process for execution by a computer, i.e., is a computer-implementable method. The various steps of the method therefore reflect various parts of a computer program, e.g., various parts of one or more algorithms.

Also, in the context of the present application, a (processing) system can be a single device or a collection of distributed devices that are adapted to execute one or more embodiments of the methods of the present invention. For instance, a system can be a personal computer (PC), a server or a collection of PCs and/or servers connected via a network such as a local area network, the Internet and so on to cooperatively execute at least one embodiment of the methods of the present invention.

Also, in the context of the present application, a system can be a single device or a collection of distributed devices that are adapted to execute one or more embodiments of the methods of the present invention. For instance, a system can be a personal computer (PC), a portable computing device (such as a tablet computer, laptop, smartphone, etc.), a set-top box, a server, or a collection of PCs and/or servers connected via a network such as a local area network, the Internet and so on to cooperatively execute at least one embodiment of the methods of the present invention.

The technical character of the present invention generally relates to data mining, and more particularly, to Association Rule Mining (ARM) mechanisms that can, for example, be employed with dynamic data (and thus be useful for recommending products and/or services). More specifically, embodiments of the present invention provide systems and methods for ARM using technical features such as a (rolling) filter bitmapping scheme for dynamic data, which addresses the issue of efficiently consuming dynamic data in a stable way and without the need to rescan the entire data. For example, in embodiments, first and second (rolling) filtering bitmaps (e.g., a Bloom filter) representing data comprising first and second variables each having a set of possible values is constructed.

Indeed, embodiments can provide efficient methods and systems for mining current max-pattern transactions (CMPT) over dynamic data. The CMPT technique can use a first and second (in-memory rolling) filtering bitmaps to cache dynamic data transactions. The first filtering bitmap can store data transactions, and the second filtering bitmap can store frequent 1-pattern itemsets. In other words, the first filtering bitmap can represent (for values of a first variable) a set of values for the second variable, while the second filtering bitmap can represent associations between frequent values of the second variable.

Accordingly, based on positional n-bit combinations per vector combinations embodiments can mine frequent (high order) k-pattern itemsets, by using mutated frequent 2-pattern itemsets. Max-pattern itemsets can then be computed by detaching sub-pattern itemsets of long-pattern itemsets.

The introduction of first and second (rolling) filtering bitmap structures can allow real time processing of all frequent datasets. However, the cost of maintaining in memory frequent itemsets is very expensive. Therefore, the memory usage can be enlarged rapidly when the amount of data available becomes larger. This can prove particularly problematic when dealing with large volumes of data, as is typical in data mining. Hence, present embodiments can provide a solution to this issue by identifying max-pattern itemsets.

A further advantage of the technical solution described above is that it can efficiently address the problem of using suitable memory bitmap structures to be able to consume dynamic continuous data in a stable way and without the need to rescan an entire database.

Embodiments can obviate or mitigate performance and stability problems associated with conventional ARM approaches, by providing a method, a system, and a computer program product for implementing association rule mining (ARM) using in-memory (rolling) filtering bitmaps over dynamic data.

By employing a filtered bit-mapping scheme over dynamic data, a space efficient and fast recommendation engine can be provided by the proposed concept(s). Embodiments of the present invention can provide a method/system for recommending a product by using in-memory rolling filtering bitmaps (e.g., Bloom filter) over dynamic data. Similarly, embodiments can implement ARM in a computer program product through the utilization of in-memory rolling filtering bitmaps over dynamic data.

A proposed embodiment can provide a computer-implemented method for association rule mining in data comprising first and second variables each having a set of possible values. The method can include, but I not limited to, generating a first filtering bitmap representing, for pluralities of values of the first variable, a set of values for the second variable, generating a second filtering bitmap representing associations between frequent values of the second variable, identifying frequent 2-pattern itemsets in the second filtering bitmap, performing first logical operations on the frequent 2-pattern itemsets to identify frequent high order-pattern itemsets; and identifying a max-pattern itemset among the frequent high-order itemsets as a mining result.

Thus, embodiments can provide an ARM method and algorithm by using the following technique steps:

(I) A composition of two bitmap filters is obtained—the first filter represents combinations two variables (e.g., products per customer) and the second filter represents combinations of one of the two variables (e.g., products between themselves). The size of both filters can depend on the total size of the transactional data records, and they can be constructed by using positional n-bits per n-blocks.

(II) After the two filters are loaded, and by working first on the second filter, the same will facilitate automatic narrowing down the final list of frequent n-itemsets based initially on a) the combinations obtained in the positional n-bits per individual block, and then b) based on the combinations obtained per total n-blocks.

(III) Then, algebraic operations may be performed between both filters to identify matches and extract the matches between the list of frequent n-itemsets from the second filter and the list of information from the first filter. In this way, a list of n-itemsets can be derived.

(IV) Finally, a max pattern itemset can be identified among the list of frequent n-itemsets.

Such a proposed concept can provide significant improvements in performance when compared to conventional ARM approaches. Further, when required to process new information (e.g., customer transactions) arriving to the database, proposed embodiments do not need to re-start the association rule mining process from the beginning. Using a rolling operation in the positional n-bits per individual block on both filters, proposed embodiments can accommodate the new transactional data without losing any of the previous calculations. In this way, the previous calculations can simply be updated. Embodiments can therefore support implementation in conjunction with dynamic data. Further, this method obviates the need to store and maintain all frequent itemsets by identifying a max pattern itemset.

By way of explanation, frequent itemsets can be itemsets with support that exceeds a predefined support threshold. The support of an itemset can be defined as the percentage of data transactions in a dataset which contain the itemset. For example, a support threshold can be 25%, meaning an itemset occurring in more than 25% of data transactions can be considered frequent.

Furthermore, an itemset X is a max pattern itemset if X is frequent and there exists no super-itemset Y (Y

X), where Y is frequent. In contrast, an itemset X is a closed pattern itemset if X is frequent and there exists no super-itemset Y

X, with the same support as X.

By way of example, according to proposed concept, there can be provided a method for ARM over dynamic data relating to customers and associated products. That is, an example where the first variable is ‘customers’ and the second variable is ‘products.’ The method can support the provision of a product recommendation using three main steps: (i) generating a first filtering bitmap (e.g., a rolling filtering bitmap) representing the set of products per customer over the dynamic data; (ii) based on the generated bitmap, generating a list of frequent itemsets; and (iii) based on the list of frequent itemsets, identifying a max pattern itemset. The method can also include the additional step of validating the generated list of itemsets (e.g., by performing one or more logical operations on the generated bitmap and the generated list of frequent itemsets).

In some embodiments, generating a first filtering bitmap can include, but is not limited to, initializing a bitmap with an initial, predetermined bit value in each position of the bitmap. Then, for each of the plurality of values of the first variable, values of the second variable can be hashed to respective positions in the first filtering bitmap. By way of example, hashing values can include, but are not limited to, responsive to the first filtering bitmap being full prior to hashing values of the second value for a next value of the first variable to the first filtering bitmap, discarding a value of the first variable from its respective discarded position in the first filtering bitmap and hashing values of the second value for the next value of the first variable to the discarded position in the first filtering bitmap.

In this way, the first filtering bitmap can remain updated while also being of a fixed size. Indeed, older data can be removed from the dataset, while new data is added in. This can facilitate the identification of frequent itemsets, and indeed a max pattern itemset, without the need to completely rescan the database upon the insertion of new data. Thus, proposed concepts can identify a max pattern itemset of dynamic data in real time.

It is understood in advance that although this disclosure includes a detailed description on cloud computing, implementation of the techniques recited herein are not limited to a cloud computing environment. Rather, embodiments of the present invention are capable of being implemented in conjunction with any other type of computing environment now known or later developed.

Cloud computing is a model of service delivery for enabling convenient, on-demand network access to a shared pool of configurable computing resources (e.g., networks, network bandwidth, servers, processing, memory, storage, applications, virtual machines, and services) that can be rapidly provisioned and released with minimal management effort or interaction with a provider of the service. This cloud model may include at least five characteristics, at least three service models, and at least four deployment models.

Characteristics are as follows:

On-demand self-service: a cloud consumer can unilaterally provision computing capabilities, such as server time and network storage, as needed automatically without requiring human interaction with the service's provider.

Broad network access: capabilities are available over a network and accessed through standard mechanisms that promote use by heterogeneous thin or thick client platforms (e.g., mobile phones, laptops, and PDAs).

Resource pooling: the provider's computing resources are pooled to serve multiple consumers using a multi-tenant model, with different physical and virtual resources dynamically assigned and reassigned according to demand. There is a sense of location independence in that the consumer generally has no control or knowledge over the exact location of the provided resources but may be able to specify location at a higher level of abstraction (e.g., country, state, or datacenter).

Rapid elasticity: capabilities can be rapidly and elastically provisioned, in some cases automatically, to quickly scale out and rapidly released to quickly scale in. To the consumer, the capabilities available for provisioning often appear to be unlimited and can be purchased in any quantity at any time.

Measured service: cloud systems automatically control and optimize resource use by leveraging a metering capability at some level of abstraction appropriate to the type of service (e.g., storage, processing, bandwidth, and active user accounts). Resource usage can be monitored, controlled, and reported providing transparency for both the provider and consumer of the utilized service.

Service Models are as follows:

Software as a Service (SaaS): the capability provided to the consumer is to use the provider's applications running on a cloud infrastructure. The applications are accessible from various client devices through a thin client interface such as a web browser (e.g., web-based e-mail). The consumer does not manage or control the underlying cloud infrastructure including network, servers, operating systems, storage, or even individual application capabilities, with the possible exception of limited user-specific application configuration settings.

Platform as a Service (PaaS): the capability provided to the consumer is to deploy onto the cloud infrastructure consumer-created or acquired applications created using programming languages and tools supported by the provider. The consumer does not manage or control the underlying cloud infrastructure including networks, servers, operating systems, or storage, but has control over the deployed applications and possibly application hosting environment configurations.

Infrastructure as a Service (IaaS): the capability provided to the consumer is to provision processing, storage, networks, and other fundamental computing resources where the consumer is able to deploy and run arbitrary software, which can include operating systems and applications. The consumer does not manage or control the underlying cloud infrastructure but has control over operating systems, storage, deployed applications, and possibly limited control of select networking components (e.g., host firewalls).

Deployment Models are as follows:

Private cloud: the cloud infrastructure is operated solely for an organization. It may be managed by the organization or a third party and may exist on-premises or off-premises.

Community cloud: the cloud infrastructure is shared by several organizations and supports a specific community that has shared concerns (e.g., mission, security requirements, policy, and compliance considerations). It may be managed by the organizations or a third party and may exist on-premises or off-premises.

Public cloud: the cloud infrastructure is made available to the general public or a large industry group and is owned by an organization selling cloud services.

Hybrid cloud: the cloud infrastructure is a composition of two or more clouds (private, community, or public) that remain unique entities but are bound together by standardized or proprietary technology that enables data and application portability (e.g., cloud bursting for load-balancing between clouds).

A cloud computing environment is service oriented with a focus on statelessness, low coupling, modularity, and semantic interoperability. At the heart of cloud computing is an infrastructure comprising a network of interconnected nodes.

Referring now to FIG. 1 , a schematic of an example of a cloud computing node is shown. Cloud computing node 10 is only one example of a suitable cloud computing node and is not intended to suggest any limitation as to the scope of use or functionality of embodiments of the invention described herein. Regardless, cloud computing node 10 is capable of being implemented and/or performing any of the functionality set forth hereinabove.

In cloud computing node 10 there is a computer system/server 12, which is operational with numerous other general purpose or special purpose computing system environments or configurations. Examples of well-known computing systems, environments, and/or configurations that may be suitable for use with computer system/server 12 include, but are not limited to, personal computer systems, server computer systems, thin clients, thick clients, hand-held or laptop devices, multiprocessor systems, microprocessor-based systems, set top boxes, programmable consumer electronics, network PCs, minicomputer systems, mainframe computer systems, and distributed cloud computing environments that include any of the above systems or devices, and the like.

Computer system/server 12 may be described in the general context of computer system-executable instructions, such as program modules, being executed by a computer system. Generally, program modules may include routines, programs, objects, components, logic, data structures, and so on that perform particular tasks or implement particular abstract data types. Computer system/server 12 may be practiced in distributed cloud computing environments where tasks are performed by remote processing devices that are linked through a communications network. In a distributed cloud computing environment, program modules may be located in both local and remote computer system storage media including memory storage devices.

As shown in FIG. 1 , computer system/server 12 in cloud computing node 10 is shown in the form of a general-purpose computing device. The components of computer system/server 12 may include, but are not limited to, one or more processors or processing units 16, a system memory 28, and a bus 18 that couples various system components including system memory 28 to processing unit 16.

Bus 18 represents one or more of any of several types of bus structures, including a memory bus or memory controller, a peripheral bus, an accelerated graphics port, and a processor or local bus using any of a variety of bus architectures. By way of example, and not limitation, such architectures include Industry Standard Architecture (ISA) bus, Micro Channel Architecture (MCA) bus, Enhanced ISA (EISA) bus, Video Electronics Standards Association (VESA) local bus, and Peripheral Component Interconnects (PCI) bus.

Computer system/server 12 typically includes a variety of computer system readable media. Such media may be any available media that is accessible by computer system/server 12, and it includes both volatile and non-volatile media, removable and non-removable media.

System memory 28 can include computer system readable media in the form of volatile memory, such as random access memory (RAM) 30 and/or cache memory 32. Computer system/server 12 may further include other removable/non-removable, volatile/non-volatile computer system storage media. By way of example only, storage system 34 can be provided for reading from and writing to a non-removable, non-volatile magnetic media (not shown and typically called a “hard drive”). Although not shown, a magnetic disk drive for reading from and writing to a removable, non-volatile magnetic disk (e.g., a “floppy disk”), and an optical disk drive for reading from or writing to a removable, non-volatile optical disk such as a CD-ROM, DVD-ROM or other optical media can be provided. In such instances, each can be connected to bus 18 by one or more data media interfaces. As will be further depicted and described below, memory 28 may include at least one program product having a set (e.g., at least one) of program modules that are configured to carry out the functions of embodiments of the invention.

Program/utility 40, having a set (at least one) of program modules 42, may be stored in memory 28 by way of example, and not limitation, as well as an operating system, one or more application programs, other program modules, and program data. Each of the operating system, one or more application programs, other program modules, and program data or some combination thereof, may include an implementation of a networking environment.

Program modules 42 generally carry out the functions and/or methodologies of embodiments of the invention as described herein. For example, some or all of the functions of a DHCP client can be implemented as one or more of the program modules 42. Additionally, the DHCP client may be implemented as separate dedicated processors or a single or several processors to provide the functionality described herein. In embodiments, the DHCP client performs one or more of the processes described herein.

Computer system/server 12 may also communicate with one or more external devices 14 such as a keyboard, a pointing device, a display 24, etc.; one or more devices that enable a user to interact with computer system/server 12; and/or any devices (e.g., network card, modem, etc.) that enable computer system/server 12 to communicate with one or more other computing devices. Such communication can occur via I/O interfaces 22. Still yet, computer system/server 12 can communicate with one or more networks such as a local area network (LAN), a general wide area network (WAN), and/or a public network (e.g., the Internet) via network adapter 20. As depicted, network adapter 20 communicates with the other components of computer system/server 12 via bus 18. It should be understood that although not shown, other hardware and/or software components could be used in conjunction with computer system/server 12. Examples, include, but are not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID (redundant array of inexpensive disks or redundant array of independent disks) systems, tape drives, and data archival storage systems, etc.

Referring now to FIG. 2 , illustrative cloud computing environment 50 is depicted. As shown, cloud computing environment 50 comprises one or more cloud computing nodes 10 with which local computing devices used by cloud consumers, such as, for example, personal digital assistant (PDA) or cellular telephone 54A, desktop computer 54B, laptop computer 54C, and/or automobile computer system 54N may communicate. Nodes 10 may communicate with one another. They may be grouped (not shown) physically or virtually, in one or more networks, such as Private, Community, Public, or Hybrid clouds as described hereinabove, or a combination thereof. This allows cloud computing environment 50 to offer infrastructure, platforms and/or software as services for which a cloud consumer does not need to maintain resources on a local computing device. It is understood that the types of computing devices 54A-N shown in FIG. 2 are intended to be illustrative only and that computing nodes 10 and cloud computing environment 50 can communicate with any type of computerized device over any type of network and/or network addressable connection (e.g., using a web browser).

Referring now to FIG. 3 , a set of functional abstraction layers provided by cloud computing environment 50 (FIG. 2 ) is shown. It should be understood in advance that the components, layers, and functions shown in FIG. 3 are intended to be illustrative only and embodiments of the invention are not limited thereto. As depicted, the following layers and corresponding functions are provided:

Hardware and software layer 60 includes hardware and software components. Examples of hardware components include mainframes 61; RISC (Reduced Instruction Set Computer) architecture based servers 62; servers 63; blade servers 64; storage device 65; and networks and networking components 66. In some embodiments, software components include network application server software 67 and database software 68.

Virtualization layer 70 provides an abstraction layer from which the following examples of virtual entities may be provided: virtual servers 71; virtual storage 72; virtual networks 73, including virtual private networks; virtual applications and operating systems 74; and virtual clients 75.

In one example, management layer 80 may provide the functions described below. Resource provisioning 81 provides dynamic procurement of computing resources and other resources that are utilized to perform tasks within the cloud computing environment. Metering and Pricing 82 provide cost tracking as resources are utilized within the cloud computing environment, and billing or invoicing for consumption of these resources. In one example, these resources may comprise application software licenses. Security provides identity verification for cloud consumers and tasks, as well as protection for data and other resources. User portal 83 provides access to the cloud computing environment for consumers and system administrators. Service level management 84 provides cloud computing resource allocation and management such that required service levels are met. Service Level Agreement (SLA) planning and fulfillment 85 provide pre-arrangement for, and procurement of, cloud computing resources for which a future requirement is anticipated in accordance with an SLA.

Workloads layer 90 provides examples of functionality for which the cloud computing environment may be utilized. Examples of workloads and functions which may be provided from this layer include: mapping and navigation 91; software development and lifecycle management 92; virtual classroom education delivery 93; data analytics processing 94; transaction processing 95; and ARM processes 96 described herein. In accordance with aspects of the invention, the ARM processes 96 workload/function operates to perform one or more of the processes described herein.

FIG. 4 depicts a cloud computing node according to another embodiment of the present invention. In particular, FIG. 4 is another cloud computing node which comprises a same cloud computing node 10 as FIG. 1 . In FIG. 4 , the computer system/server 12 also comprises or communicates with an ARM client 170, and a database 160.

In accordance with aspects of the invention, the ARM client 170 can be implemented as one or more program code in program modules 42 stored in memory as separate or combined modules. Additionally, the ARM client 170 may be implemented as separate dedicated processors or a single or several processors to provide the function of these tools. While executing the computer program code, the processing unit 16 can read and/or write data to/from memory, storage system, and/or I/O interface 22. The program code executes the processes of the invention.

By way of example, ARM client 170 may be configured to communicate database 160 via a cloud computing environment 50. As discussed with reference to FIG. 2 , for example, cloud computing environment 50 may be the Internet, a local area network, a wide area network, and/or a wireless network. In embodiments of the proposed ARM mechanism, the database 160 may provision data to the client 170. One of ordinary skill in the art would understand that the ARM client 170 and database 160 may communicate directly. Alternatively, a relay agent may be used as an intermediary to relay messages between ARM client 170 and database 160 via the cloud computing environment 50.

The present invention may be a system, a method, and/or a computer program product. The computer program product may include a computer readable storage medium (or media) having computer readable program instructions thereon for causing a processor to carry out aspects of the present invention.

The computer readable storage medium can be a tangible device that can retain and store instructions for use by an instruction execution device. The computer readable storage medium may be, for example, but is not limited to, an electronic storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the foregoing. A non-exhaustive list of more specific examples of the computer readable storage medium includes the following: a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), a static random access memory (SRAM), a portable compact disc read-only memory (CD-ROM), a digital versatile disk (DVD), a memory stick, a floppy disk, a mechanically encoded device such as punch-cards or raised structures in a groove having instructions recorded thereon, and any suitable combination of the foregoing. A computer readable storage medium, as used herein, is not to be construed as being transitory signals per se, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through a waveguide or other transmission media (e.g., light pulses passing through a fiber-optic cable), or electrical signals transmitted through a wire.

Computer readable program instructions described herein can be downloaded to respective computing/processing devices from a computer readable storage medium or to an external computer or external storage device via a network, for example, the Internet, a local area network, a wide area network and/or a wireless network. The network may comprise copper transmission cables, optical transmission fibers, wireless transmission, routers, firewalls, switches, gateway computers and/or edge servers. A network adapter card or network interface in each computing/processing device receives computer readable program instructions from the network and forwards the computer readable program instructions for storage in a computer readable storage medium within the respective computing/processing device.

Computer readable program instructions for carrying out operations of the present invention may be assembler instructions, instruction-set-architecture (ISA) instructions, machine instructions, machine dependent instructions, microcode, firmware instructions, state-setting data, or either source code or object code written in any combination of one or more programming languages, including an object oriented programming language such as Smalltalk, C++ or the like, and conventional procedural programming languages, such as the “C” programming language or similar programming languages. The computer readable program instructions may execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer may be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet Service Provider). In some embodiments, electronic circuitry including, for example, programmable logic circuitry, field-programmable gate arrays (FPGA), or programmable logic arrays (PLA) may execute the computer readable program instructions by utilizing state information of the computer readable program instructions to personalize the electronic circuitry, in order to perform aspects of the present invention.

Aspects of the present invention are described herein with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and/or block diagrams, and combinations of blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer readable program instructions.

These computer readable program instructions may be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks. These computer readable program instructions may also be stored in a computer readable storage medium that can direct a computer, a programmable data processing apparatus, and/or other devices to function in a particular manner, such that the computer readable storage medium having instructions stored therein comprises an article of manufacture including instructions which implement aspects of the function/act specified in the flowchart and/or block diagram block or blocks.

The computer readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable apparatus or other device to produce a computer implemented process, such that the instructions which execute on the computer, other programmable apparatus, or other device implement the functions/acts specified in the flowchart and/or block diagram block or blocks.

The flowchart and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of instructions, which comprises one or more executable instructions for implementing the specified logical function(s). In some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems that perform the specified functions or acts or carry out combinations of special purpose hardware and computer instructions.

FIG. 5 shows an exemplary flow diagram for performing aspects of the present invention. The steps of FIG. 5 may be implemented in the environment of FIGS. 1 and 4 , for example. As noted above, the flowchart(s) illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products as already described herein in accordance with the various embodiments of the present invention. The flowchart and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods and computer program products according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of code, which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that, in some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems that perform the specified functions or acts, or combinations of special purpose hardware and computer instructions.

Referring to FIG. 5 , there is depicted a flow diagram of a method 500 for ARM according to an exemplary embodiment. For this example, consider its application to/with a (statistically significant) sample of dynamic data transactions as defined in Table 1 below. Dynamic data transactions (row of the table) contain a value of a first variable (customer) and values of a second variable (products). Embodiments of the invention can enable ARM for the data within table 1, such that a max pattern itemset is identified.

TABLE 1 Customer Products ABC {SPSS Statistics, IoT Platform, Quantum Offering} DEF {SPSS Statistics, IoT Platform, DB2} GHI {IoT Platform, Quantum Offering, Edge Server} JKL {SPSS Statistic, IoT Platform, Quantum Offering, Edge Server} MNO {SPSS Statistics, Quantum Offering, Edge Server} PQR {SPSS Statistics, IoT Platform, Quantum Offering, Edge Server, CP4D} STU {SPSS Statistics, IoT Platform, Edge Server} VWX {SPSS Statistics, IoT Platform, Quantum Offering, DB2} . . . {. . .

In a first step 510 of the method, a first filtering bitmap representing the set of products per customer over the dynamic data can be constructed. The first filtering bitmap can be a rolling filtering bitmap (e.g., a Bloom Filter).

The first filtering bitmap can be configured to represent an initial stage of the process and can be based on the number of customers N. The size of the bitmap S, where S=((P+1)×N), can be defined based on the number of products P per itemset.

As such, the bitmap can be first initialized (in substep 512) with an initial predetermined bit value (i.e., ‘0’) in positions of the bitmap. Where the P positions of the bitmap (positional bit) can represent the SUM of a product, the data can then be hashed (i.e., mapped) to positions in the bitmap (in substep 514). In other words, for the plurality of values of the first variable, values are of the second variable are hashed to respective positions in the first filtering bitmap.

Referring to Table 1 above, and considering first filtering bitmap with size N=6, the initialized first filtering bitmap can be generated as:

000000 000000 000000 000000 000000 000000

Considering dynamic data transactions associated with customers ABC-PQR, and by adding the itemset “SPSS Statistics”, the first filtering bitmap can become:

100000 100000 000000 100000 100000 100000

Next, by adding the itemset “IoT Platform”, the first filtering bitmap can become:

110000 110000 010000 110000 100000 110000

This may be repeated for items present in the data set. As such, the fully hashed first filtering bitmap for the itemset of ABC-PQR can be generated as:

111000 110100 011010 111010 101010 111011

In some embodiments, for the hashing substep 514, if the first filtering bitmap is not full, the next/following customer can be added in the dynamic sequence to the first filtering bitmap.

Moreover, if the first filtering bitmap is full, the oldest customer can be dropped from the first filtering bitmap and a new customer can be added to the first filtering bitmap. Put another way, if the first filtering bitmap is full prior to hashing values of the second value for a next value of the first variable to the first filtering bitmap, a value of the first variable can be discarded from its respective discarded position in the first filtering bitmap, and values of the second value for the next value of the first variable can be hashed to the discarded position in the first filtering bitmap.

For example, once again referring to Table 1 above, with first filtering bitmap with size N=6. Considering a case where dynamic data transactions associated with customers STU and VWX are then input, dynamic data transactions associated with customers ABC and DEF can be deleted/dropped. This can result in the first filtering bitmap being generated as:

110010 111100 011010 111010 101010 111011

Moving onto step 520, a second filtering bitmap based on frequent values of the second variable can be generated.

In this context, the term “frequent” can mean that the itemset appears in the first filtering bitmap at a frequency greater than a support threshold. In other words, the support of an itemset can be the percentage of the dynamic data transactions in the first filtering bitmap which contain the itemset. An itemset can be labelled as frequent if its support is at least equal to a support threshold, which can be specified by a user. Referring to Table 1, the itemset {SPSS Statistics} exists in association with customers, ABC, DEF, JKL, MNO and PQR, therefore the support of {SPSS Statistics} is 5/6. Further, the itemset {SPSS Statistics, IoT Platform} exists in ABC, DEF, JKL, and PQR in the first filtering bitmap, thus support of {SPSS Statistics, IoT Platform} is 4/6.

Accordingly, at step 520 frequent 1-itemsets having a support value greater than a support threshold are identified. In reference to Table 1 and considering a support threshold of 0.2 occurrences per dynamic data transaction, this includes {SPSS Statistics}, {IoT Platform}, {Quantum Offering}, and {Edge Server}. While {DB2} occurs twice over the whole dataset, the first filtering bitmap only has a size of N=6, and therefore only one occurrence of {DB2} exists. Indeed, only one occurrence of {CP4D} exists, and so this item is identified as an infrequent 1-itemset.

The size of the second filtering bitmap S2, can be represented as (N−1)×(N−1), where N is the number of frequent 1-itemsets. Therefore, in the current example, the bitmap can have a size of 3×3.

As such, the second filtering bitmap can first be initialized (in substep 522) with an initial predetermined bit value (i.e ‘0’) in positions of the bitmap, and so can be represented as:

000 000 000

In substep 524, the first vector can be defined as the representation of the intersection of the itemset {SPSS Statistics} with the itemsets {IoT Platform}, {Quantum Offering} and {Edge Server}. Consequently, values can be hashed and the second filtering bitmap can be represented as:

111 000 000

Next, the second vector can be defined as the representation of the intersection of the itemset {IoT Platform} with the itemsets {IoT Platform}, {Quantum Offering} and {Edge Server}. Thus, the values can be hashed and the second filtering bitmap may be represented as:

111 011 000

Finally, the third vector may be used to represent the intersection of the itemset {Quantum Offering} with the itemsets {IoT Platform}, {Quantum Offering} and {Edge Server}. Therefore, the finalised second filtering bitmap may be generated as:

111 011 001

In a third step of the method provided by embodiments of the present invention, once the second filtering bitmap is full, infrequent itemsets are removed. In other words, at step 530 frequent 2-pattern itemsets can be identified in the second filtering bitmap. For example, the frequent 1-pattern itemsets {SPSS Statistics} and {IoT Platform} are sub-itemsets of the frequent 2-pattern itemset {SPSS Statistics, IoT Platform}. Consequently, by removing frequent 1-pattern itemsets out of frequent 2-pattern itemsets embodiments can obtain the final list of frequent 2-pattern itemsets as being: {SPSS Statistics, IoT Platform}, {SPSS Statistics, Quantum Offering}, {SPSS Statistics, Edge Server}, {IoT Platform, Quantum Offering}, {IoT Platform, Edge Server} and {Quantum Offering, Edge Server}.

Optionally, frequent itemsets can be validated against the first filtering bitmap calculated from the first step 510. Such validation can be undertaken by performing an AND operation between the first filtering bitmap and the list of itemsets.

That is, for the example data of Table 1, the rolling filtering bitmap calculated from the first step 510 above can be:

110010 111100 011010 111010 101010 111011

and the 2-itemsets generated can be:

{SPSS Statistics, IoT Platform}, {SPSS Statistics, Quantum Offering}, {SPSS Statistics, Edge Server}, {IoT Platform, Quantum Offering}, {IoT Platform, Edge Server} and {Quantum Offering, Edge Server}.

By performing an AND operation between the rolling filtering bitmap and the list of itemsets, it can be determined that the 2-itemset {SPSS Statistics, IoT Platform} can be represented in positions 1, 2, 4 and 6 of the rolling filtering bitmap respectively (110010, 111100, 111010 and 111011 respectively, where the first bit digit can represent “SPSS Statistics”, the second bit digit can represent “IoT Platform”). Thus, it may be verified that the itemset {SPSS Statistics, IoT Platform} is frequent (or infrequent, as may be the case). Indeed, this step can be performed for each identified itemset.

That is, the AND operation effectively can act as an operation for comparing the first filtering bitmap and the list of itemsets. Other comparison techniques can be used to determine which itemsets of the list satisfy a support threshold condition.

At step 540, first logical operations can be performed on the frequent 2-pattern itemsets to identify frequent high order-pattern itemsets.

Once again, following the example above, the frequent 2-pattern itemsets can then be extended into 3-pattern itemsets. As such, embodiments can establish the result of a logical AND operation as 1 when itemsets, for example itemset {SPSS Statistics, Quantum Offering}, are not less than a support threshold, otherwise the result can be 0 (itemset {SPSS Statistics, Quantum Offering} is marked as 0). Accordingly, the frequent 2-pattern itemset {SPSS Statistics, IoT Platform} can be initially adopted as the relative probable itemset, due to the fact that itemset {SPSS Statistics, Quantum Offering}=1 and itemset {IoT Platform, Quantum Offering}=1. Hence, it flows logically that itemset {SPSS Statistics, Quantum Offering} can be extended into itemset {SPSS Statistics, IoT Platform, Quantum Offering}. The process can be repeated until the final list of frequent 3-pattern itemsets is given.

In other words, the following rule can be used to extend the 2-itemsets to 3-itemsets:

a) {SPSS Statistics, IoT Platform} AND {SPSS Statistics, Quantum Offering} AND {IoT Platform, Quantum Offering}

→{SPSS Statistics, IoT Platform, Quantum Offering}

More generally, any 3 frequent 2-itemsets A, B and C, can be extended to a 3-itemset D:

If A∩B=B∩A and if C=((A∪B)\(A∩B)) then D=((A∩B)∪C). This rule can also be extended to any frequent n-itemsets).

Thus, the full set of 3-itemsets can be given by: {SPSS Statistics, IoT Platform, Edge Server}, {SPSS Statistics, Quantum Offering, Edge Server}, {IoT Platform, Quantum Offering, Edge Server}.

Further logical operations can be performed in step 540, in order to discover high order-pattern itemsets. Thus, continuing with the example, the frequent 3-pattern itemsets can be extended into 4-pattern itemsets. The frequent itemset {SPSS Statistics, IoT Platform, Quantum Offering} can be initially adopted as the relative probable itemset, due to the fact that itemset {SPSS Statistics, Edge Server}=1, itemset {IoT Platform, Edge Server}=1 and itemset {Quantum Offering, Edge Server}=1. Hence, it once again makes sense logically that itemset {SPSS Statistics, IoT Platform, Quantum Offering} can be extended into {SPSS Statistics, IoT Platform, Quantum Offering, Edge Server}.

Thus, the identified max pattern itemset can be identified as {SPSS Statistics, IoT Platform, Quantum Offering, Edge Server} at step 550.

As should now be understood by those skilled in the art, in embodiments of the present invention, the ARM mechanism provides numerous advantages over conventional data mining approaches. These advantages include, but are not limited to, efficient consumption of dynamic data in a stable way and without the need to rescan entire data, and a reduced memory footprint by identifying a max pattern itemset. In embodiments of the present invention, this technical solution is accomplished by using (in-memory rolling) first and second filtering bitmaps over dynamic data to identify a max pattern itemset.

In still further advantages to a technical problem, the systems and processes described herein can provide a computer-implemented method for efficient ARM with respect to multilevel knowledge-based transactional databases, and such databases can be provided on (or via) a distributed communication network. In this case, a computer infrastructure, such as the computer system shown in FIGS. 1 and 4 or the cloud environment shown in FIG. 2 can be provided and one or more systems for performing the processes of the invention can be obtained (e.g., created, purchased, used, modified, etc.) and deployed to the computer infrastructure. To this extent, the deployment of a system can can include, but is not limited to, one or more of:

(i) installing program code on a computing device, such as computer system shown in FIG. 1 , from a computer-readable medium;

(ii) adding one or more computing devices to the computer infrastructure and more specifically the cloud environment; and

(iii) incorporating and/or modifying one or more existing systems of the computer infrastructure to enable the computer infrastructure to perform the processes of the invention.

The descriptions of the various embodiments of the present invention have been presented for purposes of illustration, but are not intended to be exhaustive or limited to the embodiments disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The terminology used herein was chosen to best explain the principles of the embodiments, the practical application or technical improvement over technologies found in the marketplace, or to enable others of ordinary skill in the art to understand the embodiments disclosed herein. 

1. A computer-implemented method for association rule mining in data comprising first and second variables each having a set of possible values, the method comprising: generating a first filtering bitmap representing, for each of a plurality of values of the first variable, a set of values for the second variable; generating a second filtering bitmap representing associations between frequent values of the second variable; identifying frequent 2-pattern itemsets in the second filtering bitmap; performing first logical operations on the frequent 2-pattern itemsets to identify frequent high order-pattern itemsets; and identifying a max pattern itemset among the frequent high-order itemsets as a mining result.
 2. The computer-implemented method of claim 1, wherein identifying a frequent itemset comprises: performing a second logical operation with the first filtering bitmap and the itemset; assessing the second logical operation result with a support threshold to determine whether to identify the itemset as frequent.
 3. The computer-implemented method of claim 1, wherein generating the first filtering bitmap comprises: initializing a bitmap with an initial, predetermined bit value in each position of the bitmap; and for each of the plurality of values of the first variable, hashing values of the second variable to respective positions in the first filtering bitmap.
 4. The computer-implemented method of claim 3, wherein hashing values comprises: responsive to the first filtering bitmap being full prior to hashing values of the second variable for a next value of the first variable to the first filtering bitmap, discarding a value of the first variable from its respective discarded position in the first filtering bitmap and hashing values of the second variable for the next value of the first variable to the discarded position in the first filtering bitmap.
 5. The computer-implemented method of claim 1, wherein generating the second filtering bitmap comprises: initializing a bitmap of size (N−1)×(N−1), where N is equal to a number of frequent values for the second variable; and for each of a set frequent values of the second variable, hashing frequent values of the second variable to respective positions in the bitmap.
 6. The computer-implemented method of claim 1, wherein the first variable is configured to represent a customer and wherein the second variable is configured to represent a product.
 7. The computer-implemented method of claim 1, wherein the data comprises dynamic data.
 8. A computer program product for association rule mining in data comprising first and second variables each having a set of possible values, the computer program product comprising a computer readable storage medium having program instructions embodied therewith, the program instructions executable by a processing unit to cause the processing unit to perform a method comprising: generating a first filtering bitmap representing, for each of a plurality of values of the first variable, a set of values for the second variable; generating a second filtering bitmap representing associations between frequent values of the second variable; identifying frequent 2-pattern itemsets in the second filtering bitmap; performing first logical operations on the frequent 2-pattern itemsets to identify frequent higher order-pattern itemsets; and identifying a max pattern itemset among the frequent higher-order itemsets as a mining result.
 9. The computer program product of claim 8, wherein identifying a frequent itemset comprises: performing a second logical operation with the first filtering bitmap and the itemset; assessing the second logical operation result with a support threshold to determine whether to identify the itemset as frequent.
 10. The computer program product of claim 8, wherein generating the first filtering bitmap comprises: initializing a bitmap with an initial, predetermined bit value in each position of the bitmap; and for the plurality of values of the first variable, hashing values of the second variable to respective positions in the first filtering bitmap.
 11. The computer program product of claim 10, wherein hashing values comprises: responsive to the first filtering bitmap being full prior to hashing values of the second value for a next value of the first variable to the first filtering bitmap, discarding a value of the first variable from its respective discarded position in the first filtering bitmap and hashing values of the second value for the next value of the first variable to the discarded position in the first filtering bitmap.
 12. The computer program product of claim 8, wherein generating the second filtering bitmap comprises: initializing a bitmap of size (N−1)×(N−1), where N is equal to the number of frequent values for the second variable; and for each of a set of frequent values of the second variable, hashing frequent values of the second variable to respective positions in the bitmap.
 13. The computer program product of claim 8, wherein the first variable is configured to represent a customer and wherein the second variable is configured to represent a product.
 14. The computer program product of claim 8, wherein the data comprises dynamic data.
 15. A system for association rule mining in data comprising first and second variables each having a set of possible values, the system comprising: a processor arrangement configured to perform the steps of: generating a first filtering bitmap representing, for each of a plurality of values of the first variable, a set of values for the second variable; generating a second filtering bitmap based on frequent values of the second variable; identifying frequent 2-pattern itemsets in the second filtering bitmap; performing first logical operations on the frequent 2-pattern itemsets to identify frequent higher order-pattern itemsets; and identifying a max pattern itemset among the frequent higher-order itemsets as a mining result.
 16. The system of claim 15, wherein identifying a frequent itemset comprises: performing a second logical operation with the first filtering bitmap and the itemset; assessing the second logical operation result with a support threshold to determine whether to identify the itemset as frequent.
 17. The system of claim 15, wherein generating the first filtering bitmap comprises: initializing a bitmap with an initial, predetermined bit value in each position of the bitmap; and for each of the plurality of values of the first variable, hashing values of the second variable to respective positions in the first filtering bitmap.
 18. The system of claim 17, wherein hashing values comprises: responsive to the first filtering bitmap being full prior to hashing values of the second value for a next value of the first variable to the first filtering bitmap, discarding a value of the first variable from its respective discarded position in the first filtering bitmap and hashing values of the second value for the next value of the first variable to the discarded position in the first filtering bitmap.
 19. The system of claim 15, wherein generating the second filtering bitmap comprises: initializing a bitmap of size (N−1)×(N−1), where N is equal to the number of frequent values for the second variable; and for each of a set frequent values of the second variable, hashing frequent values of the second variable to respective positions in the bitmap.
 20. The system of claim 15, wherein the data comprises dynamic data. 